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Given:
[tex]\[ h(x) = 0.000371\left(x^2 - 1280x\right) + 152 \][/tex]

The Golden Gate Bridge is a suspension bridge with two cables hung from two towers of equal height that are 1,280 meters apart. The function models [tex]\( h \)[/tex], the height of each cable above the ground in meters, as it relates to [tex]\( x \)[/tex], the cable's horizontal distance from the left tower in meters. What is the height of the towers in meters?

Choose one answer:
(A) 640
(B) 152
(C) 0.000371
(D) 198

Sagot :

GinnyAnswer
Let's analyze the given function:

[tex]\[ h(x) = 0.000371(x^2 - 1280x) + 152 \][/tex]

This function represents the height [tex]\( h \)[/tex] of the cable above the ground as it relates to [tex]\( x \)[/tex], the horizontal distance from the left tower. To find the height of the towers, we need to determine the height at the point where [tex]\( x = 0 \)[/tex].

Step-by-Step Solution:

1. Substitute [tex]\( x = 0 \)[/tex] into the function:

[tex]\[ h(0) = 0.000371(0^2 - 1280 \times 0) + 152 \][/tex]

2. Simplify the expression inside the parentheses:

[tex]\[ h(0) = 0.000371(0 - 0) + 152 \][/tex]
[tex]\[ h(0) = 0.000371 \times 0 + 152 \][/tex]

3. Since [tex]\( 0.000371 \times 0 = 0 \)[/tex], the equation simplifies to:

[tex]\[ h(0) = 0 + 152 \][/tex]
[tex]\[ h(0) = 152 \][/tex]

Therefore, the height of the towers is [tex]\( 152 \)[/tex] meters.

So the correct answer is:

(B) 152
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